I have 3 types of cuddly toy on my bedroom shelf: a teddy, a giraffe and a panda.
a. How many different ways can I arrange them on my shelf?
b. If I buy another teddy identical to the first, how many different ways can I now arrange them?
If you think about the three toys - any one can be put down first ie three choices. Then when that is done there are two choices for the second toy so 3 x 2 x 1
The second is more tricky - with four different toys it would be 4 x 3 x 2 x 1 but some of them look the same because the two bears are identical. If I call the teddies T you can see I get some duplicates:
ie 12 ways - the theory says (4 x 3 x 2 x 1) divided by (2 x 1) because two are identical and we can ignore these.